f-Class two graphs whose f-cores have maximum degree two.

An f-coloring of a graph G is an edge-coloring of G such that each color appears at each vertex ν ∈ V ( G) at most f( ν) times. The f-core of G is the subgraph of G induced by the vertices ν of degree $d(v) = f(v)\max _{v \in V(G)} \{ \left\lceil {d(v)/f(v)} \right\rceil \} $. In this paper, we find some necessary conditions for a simple graph, whose f-core has maximum degree two, to be of class 2 for f-colorings. [ABSTRACT FROM AUTHOR]